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Tuesday, October 05, 2004

Although I disagreed with Lance and Jeff on whether theory folks are too nice to ask hard questions, let us assume for argument's sake that there is some merit to this argument (there definitely is some just in comparison with other non-CS fields). What might be the cause of this restraint ?

A distinct possibility is the fairly objective nature of our discipline itself. Suppose that tomorrow I present a paper describing an algorithm that can do range searching on collections of fetid schizoid tapeworms in logarithmic time. Now, what is clearly true is that my algorithm takes logarithmic time; about this there can be no objection. However, it is likely that some folks will find the area of fetid schizoid tapeworms somewhat uninteresting; they might be partial towards energetic mobile ringworms instead. There might still be others that claim that most schizoid tapeworms are merely malodorous, for which logarithmic time range searching queries are trivial.

However, they cannot dispute the objective validity of my algorithm, and their dislike of my choice of object is not in itself objectively defensible.

This, to me, is one possible reason why theoreticians don't argue so much. It is not that we don't have strong opinions; if you talk to people one-on-one they will often criticize results based on non-technical reasons. It is that maybe people are less comfortable with non-formal reasoning processes.

Aha, but then you will say that "pure" mathematicians should not be the cantankerous bunch that they often can be. Indeed. However, theoretical computer science is most close in spirit to combinatorics, a field defined not by a foundational structure of axioms and theorems, but by a myriad of problems all connected together in countless different ways. It is hard to make objective judgements about the value of problems; most problems are quite interesting to think about in the abstract, at least to someone. It is a lot easier to evaluate the quality of a theoretical edifice, and in fact one of the knocks on combinatorics is precisely the "apparent" lack of such an edifice.